TIME SERIES AND FINANCIAL TIME SERIES

Course objectives

The course aims at showing, both from a graphical point of view and from a methodological one, the main tools for analyzing economic and financial time series. Students will also learn to use to the statistical software R as a tool for applying statistical methodologies to real data, as well as for understanding the theory behind a model. Students who pass the exam will know the main concepts and procedures for model building when analyzing economic and financial time series. Students who pass the exam will have skills for data analysis: on the basis of the methodologies introduced in the course and of the knowledge of the R software tools, they will be able to choose the best model to represent real economic and financial phenomena. Starting from real data they will be able to find the best strategy to represent data. They will also be able to analyze in a critical way the obtained results, highlighting pros and cons of the chosen procedures. Students’ skills are stimulated by tackling real case studies and developing a research project which will be discussed in class. The evaluation of the report will also concern students’ communication skills and their ability to explain what they learned and the results of the quantitative analysis. The deep comprehension of the learned methodologies, will allow the student to understand more general models not explained in the course, evaluating advantages and disadvantages.

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Program - Frequency - Exams

Course program
Part I. Elements of Statistical Inference. - Inferential problems and the statistical model; - Likelihood function; - MLEs and properties; - Observed/expected Fisher information; - Likelihood sets, confidence intervals; - Hypothesis testing. Part II. Time series and descriptive statistics. - Definition and examples - Descriptive statistics and graphical analysis - The components: trend, seasonality, and error term. - How to eliminate the trend the seasonality Part III. Properties of Time Series Processes. - Mean, Variance, ACF and PACF - Main properties: stationarity, ergodicity and invertibility - Lag operator Part IV. Models and properties. - Mean models: AR(p), MA(q), ARMA(p,q), ARIMA(p,d,q), SARIMA and properties - Financial data: stylized facts - Volatility models: ARCH, GARCH and properties Part V. Choice and use of the model. - Procedure of Box & Jenkins + AIC/BIC - Unit root tests (AR, ARMA) - Residual analysis - ARCH tests, Normality tests - Parameter estimation Part VI. Prediction / Forecasting and uncertainty quantification through prediction intervals During classes, we will use the software R.
Prerequisites
- Mathematics: elementary operations with particular attention to logarithms and exponents and their properties; numerical series (especially geometric, truncated geometric); derivatives/integrals - Probability/Statistics: operators like mean, variance, covariance, correlation, and their properties; law of iterated expectations; PDF, CDF, quantiles, conditional densities - Inference: the concept of estimation, estimators and their properties (point estimators, interval estimators, and tests + properties, MLE, Fisher information -- briefly recapped at the beginning of the course); regression and OLS; skewness and kurtosis; known distributions (Binomial, Gaussian, Student-t, Chi-squared) - Stochastic Processes: the concept of process vs. random variable, Gaussian processes, white noise, random walk (concepts are revisited during the course). - Experience with R software
Books
The necessary resources will be shared by the professor during the course. The following textbooks are adopted: - Ruppert & Matteson – Statistics and Data Analysis for Financial Engineering: with R Examples (2015). Main book of reference, with R instructions. Refer to Chapters 1, 2, 4, 12, 13, 14. - Wei, Time Series Analysis (2006). This book contains several proofs we will cover during the course. Refer to Chapters 1-4. Slides and video tutorials will be shared during the course.
Frequency
In-person attendance and resource sharing on the dedicated webpage
Exam mode
The evaluation will be based on a final examination (written and possibly oral), in addition to intermediate assignments.
Lesson mode
Classes will be based on an in-person type of teaching. A mixed-use of presentations, board and statistical software will be adopted.
  • Lesson code10592627
  • Academic year2024/2025
  • CourseFinance and insurance
  • CurriculumFinancial risk and data analysis - in lingua inglese
  • Year2nd year
  • Semester1st semester
  • SSDSECS-S/01
  • CFU9
  • Subject areaAttività formative affini o integrative